The theory of complex dynamics is usually applied to compare the global convergence
properties of different iterative methods, by obtaining the attraction basins for simple
polynomial equations in the complex domain. ...[+]

The theory of complex dynamics is usually applied to compare the global convergence
properties of different iterative methods, by obtaining the attraction basins for simple
polynomial equations in the complex domain. However, in this work, we use it in quite
another context: the study of a nontrivial nonlinear system that describes the motion of
interacting bodies in celestial mechanics, namely, Newtonian planar circular restricted
four-body problem and its relative equilibrium solutions. These have been investigated
from a dynamical point of view. New properties of the solutions of this system have been
obtained. Practical guidelines for efficient search of relative equilibrium solutions of Nbody
problem have been given.[-]